Fiber lasers emitting in the 3-5 μm wavelength range have attracted much interest during the last years, thanks to their wide potential employment in different fields, such as remote sensing, air pollution detection, communication applications, and medical diagnostics. Fluoroindate fibers allow transmission in this range and can be doped with different rare-earth ions, including erbium, holmium, dysprosium, and neodymium. Recent experiments have shown the feasibility of emission at λ = 3.92 μm wavelength employing Ho:Nd co-doped fluoroindate glass, encouraging the investigation on continuous-wave (CW) emission lasers. In this work, a complete model of Ho:Nd co-doped fluoroindate fiber pumped at λp = 808 nm and emitting at λ = 3920 nm is developed, in order to find the unknown energy transfer parameters, thus allowing a correct design. The energy transfer parameter recovering is performed by simulating the fluoroindate fiber via a finite element method (FEM) code, by solving the rate equations with a homemade code and by matching simulations with experimental values reported in literature. The results pave the way for the accurate design of a CW laser emitting at λ = 3920 nm, potentially with better efficiency than lasers based on Ho3+ -heavily-doped fluoroindate fibers. Preliminary fiber laser design has been based on commercially available fluoroindate fibers, including double cladding fibers, in order to choose the best geometry for the fiber laser and investigate its feasibility.
A novel fiber laser based on a fluoroindate glass doped with erbium ions and cladding pumped with red light is designed. In the simulation, the pump beam at 635 nm wavelength is injected in a commercially available double D-shaped, fewmode, optical fiber fabricated by Le Verre Fluoré in order to excite the 4F9/2 energy level. A strong population inversion between 4F9/2 and 4I9/2 energy levels is obtained, thus allowing emission in the 3400-3600 nm band. The electromagnetic analysis of the fiber, performed by the finite element method, shows that up to six signal modes at 3500 nm are supported. An exhaustive mathematical model based on five rate equations for the erbium ion populations, coupled with the power propagation equations for the pump and all the signal modes, is developed. Both cases of forward and bidirectional pumping are considered. All the spectroscopic parameters employed in the model, including the absorption/emission cross sections, the lifetimes and the branching ratios, are taken from the literature. The numerical code allows for evaluating the output signal power, the threshold pump power, and the slope efficiency. The behavior of the laser is studied by varying several parameters, such as the cavity length, the erbium concentration and the output mirror reflectivity. Preliminary simulations show that, with pump powers of a few hundred mW, lasing can be obtained. These results will be improved by using an evolutionary optimization technique, like the particle swarm optimization approach, and promise interesting low-cost applications.
The accurate knowledge of the rare-earth spectroscopic parameters is fundamental for the design of both fiber and integrated active devices. The lifetimes, the branching ratios, the up-conversion, the cross-relaxation, the energy transfer coefficients of the rare-earths must be preliminarily identified before the design. The particle swarm optimization (PSO) is an efficient global search approach; when applied to rare-earth-doped host materials and devices, it permits the rare-earth spectroscopic characterization starting from optical gain measurements. The model for the peculiar case of a SiO2 - SnO2 : Er3+ glass ceramic system is illustrated. Two different, direct and indirect, pumping schemes are considered for the rare-earth spectroscopic characterization. In the direct pumping scheme, a pump at 378 nm wavelength is used to excite the erbium ions. The SnO2 does not take part in the excitation process. On the contrary, in the indirect pumping scheme the SnO2 is involved by exploiting the absorption band around 307 nm wavelength via a proper pump. In this case, the energy transfer between the SnO2 and the Er3+ ions occurs during the amplification process. The fabricated SiO2 - SnO2 : Er3+ glass ceramic slab waveguide is simulated via a finite element method (FEM) code and a homemade code is used to solve the rate equations. In order to identify the value of the SnO2-Er3+ energy transfer coefficient, the ratio between the two simulated optical gains at 1533 nm wavelength, with the direct and indirect pumping schemes, is compared with the ratio between the two emission intensity measurements.
The theoretical model of rare earth doped optical devices based on the rate equations and the power propagation equations can be employed for recovering, via an indirect approach, the rare earth spectroscopic parameters. As an example, the model for an erbium doped silica-tin dioxide, SiO2 - SnO2 : Er3+, glass ceramic waveguide is considered. Two different pumping schemes are employed to excite the erbium ions, the direct pumping at 378 nm and the indirect pumping at 307 nm via the tin dioxide. The achievable optical gain per unit length at 1533 nm is then evaluated for both pumping cases. The ratio between the two simulated optical gains is compared with the emission intensity measurements to estimate the value of the SnO2-Er3+ energy transfer coefficient. The particle swarm optimization algorithm is applied in order to find the SiO2 - SnO2 : Er3+ glass ceramic spectroscopic parameters which properly match the simulated optical gains ratio with the experimentally measured emission ratios. In the same way, the pump power coupled in the glass ceramic waveguide is also recovered. The SnO2-Er3+ energy transfer coefficient is estimated to be about 6.1 × 10-22 m3/s.
SnO2-based glass-ceramics activated by rare earth ions have been extensively investigated because of the need to develop reliable fabrication protocols and clarify some interesting optical, structural, and spectroscopic features of the system. There is one important weakness in glass photonics when the rare earth ions are employed as luminescent sources. This is the low absorption cross section of the electronic states of the rare earth ions. A sensitizer is therefore requested. In the last years, we demonstrated that SiO2-SnO2 glass ceramics, presenting a strong absorption cross section in the UV range due to the SnO2 nanocrystal, are effective rare earth ions sensitizers. Another interesting property of the SiO2-SnO2 system is its photorefractivity. The high photorefractivity of sol-gel-derived SnO2-SiO2 glass-ceramic waveguides has been demonstrated in several papers published by our consortium. It has been shown that the UV irradiation induces refractive index change allowing the direct writing of both channel waveguides and Bragg gratings.
The results presented in this communication not only demonstrate the viability and outstanding properties of the SiO2- SnO2 glass-ceramics for photonic applications but also put the basis for the fabrication of solid state and integrated lasers. The next steps of the research are the fabrication of the channels and mirrors exploiting the photorefractivity as well as to draw glass ceramic fiber, checking the lasing action and corresponding functional characteristics. Finally, it is worth noting that the dynamic of the energy transfer from the nanocrystals to the rare earth ions is still an exciting open question.
The paper illustrates both review and original simulation results obtained via the modelling of different set-ups based on optical microresonators for applications in optical sensing, lasing and spectroscopy. Passive microbubbles and microspheres coupled via long period fiber gratings (LPGs) and tapered fibers are designed and/or constructed for sensing of biological fluids in the near infrared (NIR) wavelength range. Rare earth doped chalcogenide glass integrated microdisks are designed for active sensing in the medium infrared (MIR) wavelength range. A home-made numerical code modelling the optical coupling and the active behavior via rate equations of ion population is employed for a realistic design, by taking into account the most important active phenomena in rare earths, such as the absorption rates, the stimulated emission rates, the amplified spontaneous emission, the lifetime and branching ratios, the ion-ion energy transfers and the excited state absorption. Optical coupling is obtained by employing ridge waveguides, for micro-disks, and tapered fibers, for microspheres and microbubbles. Different dopant rare earths as Erbium (Er3+) and Praseodymium (Pr3+) are considered.
The modeling and design of fiber lasers is an essential element of their development process. One of the areas of particular interest during the last years is the development of lanthanide ion-doped fiber lasers which operate at wavelengths exceeding 2000 nm. There are two main host glass materials developed for this purpose: fluoride and chalcogenide. One of the main specific aims of this contribution is therefore to comparatively study the properties of various numerical algorithms applicable to the design and modeling of fiber lasers operating at wavelengths exceeding 2000 nm. Hence, the convergence properties of selected algorithms implemented within various software environments are studied with a particular focus on the CPU time and calculation residual.
A Dy3+-doped ZBLAN fiber amplifier based on an in-band pumped configuration is designed and optimized via an evolutionary approach. In the proposed model, the rate equations are coupled with the power propagation equations for the pump and signal beams. The complete amplifier model allows the definition of the fitness function to be optimized. Realistic values for optical and spectroscopic parameters are considered. For a fiber with dopant concentration of 2000 ppm, by employing an input pump power of 1 W at 2.72 μm wavelength, an optical gain of about 15.56 dB at 2.95 μm wavelength is obtained.
The design of two pumping schemes for mid-IR lasers based on photonic crystal fibers (PCFs) is illustrated. The PCFs considered in both pumping schemes are made of dysprosium-doped chalcogenide glass Dy3+:Ga5Ge20Sb10S65. The two optical sources are accurately simulated by taking into account the spectroscopic parameters measured on a rare earth-doped glass sample. A home-made numerical model based on power propagation equations and solving the ion population rate equations of the rare earth is developed and employed to perform a feasibility investigation. The first pumping scheme is based on optical power pumping at 1700 nm wavelength and allows beam emission close to 4400 nm wavelength, the efficiency is increased till about η = 22% by integrating a suitable optical amplifier after the laser cavity. The second pumping scheme exploits two pump beams at the wavelengths close to 2800 nm and 4100 nm and enables a laser emission close to 4400 nm wavelength with an efficiency higher than η = 30%. Both these sources could promote a number of promising applications in different areas such as satellite remote sensing, laser surgery, chemical/biological spectroscopy and mid-IR optical communication.
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